Specifically, for \(m \le n\) , we consider the special case \(\bar{{\bf H}}\bar{{\bf H}}\mathsf {^H}= h{\bf I}\)  (for \(m> n\)  we assume \(\bar{{\bf H}}\mathsf {^H}\bar{{\bf H}} = h{\bf I}\) ), where \(h\)  is a positive parameter. This
assumption reflects two main settings: the scalar LOS channel, introduced in [1]} and
therein already analysed in the high-SNR regime, and the LOS MIMO with residual scattering
[2]}. Both models assume the LOS matrix to have high (full) rank. The one in [2]} is
suitable for MIMO backhaul links where antenna spacing is carefully designed and transmit-receive
distance is fixed. Our model can be thought of as a Gaussian perturbation, with small variance, of
the one in [2]}. The model in [1]}, although being a sub-case of the one in
[2]} from the pure mathematical viewpoint, has played a major role in the early
characterization of MIMO Rician channels, due to the amenability of diagonal [7]} (and, in
particular, scalar) non-centrality matrices for the derivation of the capacity-achieving input law.
